Single carrier with cyclic prefix (“CP-SC”) insertion is a signal format known in the art for facilitating frequency-domain equalization. This is due to the cyclic prefix insertion causing the convolution of the CP-SC signal with a multipath channel to appear circular at the receiver (this can also be said to restore orthogonality between the frequency domain bins or subcarriers of a frequency domain representation of the signal). This circular appearance of the channel (also known as a circular channel) enables the use of low complexity frequency-domain equalization of the single carrier signal. However, a disadvantage of conventional CP-SC is that the receiver discards the received cyclic prefix prior to detection, resulting in a waste of the energy relating to the cyclic prefixes.
Training prefix single carrier is a means to recover the lost energy relating to the cyclic prefixes. Training prefix single carrier replaces the traditional cyclic prefixes with a block of known symbols known as the training prefix (i.e., each block of data symbols has a training prefix sent before and after it, where the one after it is actually a prefix for a following data block). Also, the training prefix is the same for each block of data symbols. These training symbols may be used to estimate the channel or improve the tracking in time of the channel. However, prior art methods for recovering the data symbols may be inefficient due to the need of taking a larger fast fourier transform (“FFT”) that encompasses the training prefixes. Finally, prior art methods will not work when the training prefix before a block of data symbols is different than the training prefix after the block of data symbols.
Therefore, it is desirable to receive the advantages of the training prefix single carrier signal while maintaining the circular channel property of conventional CP-SC. It would also be beneficial to develop techniques that can be used with multi-carrier systems such as OFDM.